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arXiv · 2205.04151

Learning effective dynamics from data-driven stochastic systems

Lingyu Feng·Ting Gao·Min Dai·Jinqiao Duan
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Abstract

Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to investigating the effective dynamics for slow-fast stochastic dynamical systems. Given observation data on a short-term period satisfying some unknown slow-fast stochastic systems, we propose a novel algorithm including a neural network called Auto-SDE to learn invariant slow manifold. Our approach captures the evolutionary nature of a series of time-dependent autoencoder neural networks with the loss constructed from a discretized stochastic differential equation. Our algorithm is also validated to be accurate, stable and effective through numerical experiments under various evaluation metrics.

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Lingyu Feng, Ting Gao, Min Dai, Jinqiao Duan. 2022-05-09. Learning effective dynamics from data-driven stochastic systems. https://doi.org/10.1063/5.0126667

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